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Multivariate sequential point estimation

Author

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  • Ghosh, Malay
  • Sinha, Bimal K.
  • Mukhopadhyay, Nitis

Abstract

For a multivariate normal distribution with unknown mean vector and unknown dispersion matrix, a sequential procedure for estimating the unknown mean vector is suggested. The procedure is shown to be asymptotically "risk efficient" in the sense of Starr (Ann. Math. Statist. (1966), 1173-1185), and the asymptotic order of the "regret" (see Starr and Woodroofe, Proc. Nat. Acad. Sci. 63 (1969), 285-288) is given. Moderate sample behaviour of the procedure using Monte-Carlo techniques is also studied. Finally, the asymptotic normality of the stopping time is proved.

Suggested Citation

  • Ghosh, Malay & Sinha, Bimal K. & Mukhopadhyay, Nitis, 1976. "Multivariate sequential point estimation," Journal of Multivariate Analysis, Elsevier, vol. 6(2), pages 281-294, June.
    • Handle: RePEc:eee:jmvana:v:6:y:1976:i:2:p:281-294
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    Citations

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    Cited by:

    1. N. Mukhopadhyay & A.D. Abid, 1999. "Accelerated sequential shrinkage estimation," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1-2), pages 159-171.
    2. Nitis Mukhopadhyay & Srawan Kumar Bishnoi, 2020. "On general asymptotically second-order efficient purely sequential fixed-width confidence interval (FWCI) and minimum risk point estimation (MRPE) strategies for a normal mean and optimality," METRON, Springer;Sapienza Università di Roma, vol. 78(3), pages 383-409, December.
    3. N. Mukhopadhyay & G. Vik, 1986. "Sequential simultaneous estimation of the mean and variance: The rate of convergence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 33(1), pages 291-297, December.

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